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Approximation-solvability of a system of generalized nonlinear mixed variational inequalities. (English) Zbl 1076.49004
Summary: We introduce and study a new class of systems of generalized nonlinear mixed variational inequalities and prove its equivalence with a class of fixed-point problems by making use of the properties of the subdifferential of a proper, convex and lower semi-continuous functional. We also construct a new iterative algorithm for solving this class of systems of inequalities and prove the existence and uniqueness of solutions and the convergence of iterative sequences generated by the algorithm.
MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces